PSI - Issue 2_A

390 Yuri Petrov et al. / Procedia Structural Integrity 2 (2016) 389–394 Author name / Structural Integrity Procedia 00 (2016) 000 – 000 where ( ) is time-dependent loading, Ω ( ) − varying specimen geometry, ( ) − crack length which changes with time and ( )̇ = / is crack velocity. Right part of the expression (1) – − is called dynamic fracture toughness which is usually regarded to be function of loading rate ( )̇ = / , temperature and other material properties. According to classic dynamic fracture mechanics function is supposed to be defined from experiments a priori . Such approach is widely spread in the field of dynamic fracture research. However multiple experimental results (e.g. obtained in Ravi-Chandar et al. (1984), Kobayashi et al. (1997), Kalthoff (1983)) call into question analyses based on criterion (1) and existence (or at least uniqueness) of crack velocity – stress intensity factor dependence in particular. In K. Ravi-Chandar and W. Kauss (1984) it has been shown that almost constant values of crack speed may correspond to significant change of SIF in case of explicitly dynamic sample loading. The authors of these papers supposed energy flux to the crack tip to be unrelated to crack velocity, but to influence fracture surface pattern. On the other hand existence of clear and ( )̇ − ( ) dependence is observed in Kobayashi et al. (1977) and Kalthoff (1983) where precracked specimens of various geometry were loaded quasistatically. However, Kobayashi and Kalthoff note that such dependence might not be unique for particular materials and might be influenced by shape of specimens. On the other hand many experimental data confirm existence of stable dependence of crack velocity ( )̇ on crack length ( ) (which can be regarded as dependence on SIF ~ √ ). This effect was observed in Fineberg et al. (1992) and Sharon and Fineberg (1999) where experiments on thin PMMA plates are described. Generally speaking, the crack behaviour observed in works by Ravi-Chandar, Kobayashi, Dally and Kalthoff does not contradict principles laying beneath condition (1) however one will encounter problem of determination of a functional from right part of (1) as this procedure might be very complicated. Besides this classic fracture criteria similar to (1) do not consider instabilities in dependencies of fracture toughness on ( )̇ . Such diversity in experimental data on crack velocity – SIF dependence implies that stress intensity factor should not be treated as parameter which completely defines dynamic behaviour of the crack. In this paper we summarize results for research of dynamic crack propagation for various loading conditions and in addition to this first results on investigation of ( )̇ − ( ) dependence using incubation time fracture criterion are presented. Experiments on various loading conditions (from explosion-like loading of crack faces to quasistatic stretching of specimens with initial crack) have been successfully simulated using finite element method with imbedded incubation time fracture criterion. The corresponding dynamic fracture theory was developed in Petrov (1996), Petrov and Morozov (1994), Petrov et al. (2003). 2 2.1. Incubation time fracture criterion Incubation time criterion for brittle fracture at a point at time reads as 1 ∫ − 1 ∫ ( ′ , ′ ) ′ ′ ≤ − (2), where is the microstructural time of a fracture process (or fracture incubation time) a parameter characterizing the response of the studied material to applied dynamic loads (i.e. is constant for a given material and does not depend on problem geometry, the way a load is applied, the shape of a load pulse and its amplitude). is the characteristic size of a fracture process zone and is constant for the given material and the chosen scale level. is normal stress at a point, changing with time and is its critical value (ultimate stress or critical tensile stress found in quasistatic conditions). x ′ and are the local coordinate and time Characteristic size is calculated according to the following formula = 2 2 2 (3), 2. Fracture criterion and simulation technique